Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26022977 | C2 | semidirect |
| 3. #26018921 | C2 | semidirect |
| 4. #26018812 | C2 | semidirect |
| 5. #26018112 | C2 | semidirect |
| 6. #26018081 | C2 | semidirect |
| 7. C89×#1963 | C2 | semidirect |
| 10. #19151974 | C4 | semidirect |
| 11. #19151946 | C4 | semidirect |
| 48. C4×#10623494 | C2×C4 | semidirect |
| 53. C4⋊Q8×C89 | C2×C4 | semidirect |
| 54. #127×C89 | C2×C4 | semidirect |
| 119. C42×C89 | D8 | semidirect |
| 214. #1963 | D89 | semidirect |
| 219. C89 | #9299 | semidirect |
| 246. C4⋊Q8 | C4×D89 | semidirect |
| 251. #127 | C4×D89 | semidirect |
| 331. C42 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031167 | 2 |
| #26022977 | 2 |
| #26018921 | 2 |
| #26018812 | 2 |
| #26018112 | 2 |
| #26018081 | 2 |
| C89×#1963 | 2 |
| #9299 | 89 |